Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. 8. definition: a set a is finite if there exists a

8. Definition: A set A is finite if there exists a non-negative integer c such that...

80.2K

Verified Solution

Question

Advance Math

8. Definition: A set A is finite if there exists a non-negativeinteger c such that there exists a bijection from A to {n ? N : n ?c}. (The integer c is called the cardinality of A.)

(a) Let A be a finite set, and let B be a subset of A. Provethat B is finite. (Hint: induction on |A|. Note that our proofcan’t use induction on |B|, or indeed refer to “the number ofelements in B” at all, because we don’t yet know that B isfinite!)

(b) Prove that the union of two disjoint finite sets isfinite.

(c) Prove that the union of any two finite sets is finite.(Hint: A ? B = A ? (B ? A))

Answer & Explanation Solved by verified expert
4.3 Ratings (618 Votes)
Denote c n in N n c 1234c then c c is the cardinality of thefinite set ca let A be a finite set and assume that B is a finite subsetof A If B is empty then B is finite So we assume that B isnonemptySince A is finite there exists a    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Q

Select the correct answer from each drop-down menu.Ben and Carmella want to go to a...

Algebra
Q

Rothamsted Experimental Station (England) has studied wheat production since 1852. Each year, many small plots of...

Basic Math
Q

the key objective of risk management is to increase the probability of a project achieving its...

Civil Engineering
Q

A simple pendulum of length 1 metre suspended from the ceiling of a lift executes...

Physics
Q

On a recent quiz the class mean was 72 with a standard deviation of 3...

Statistics
Q

**Case Study: XYZ Corporation - Accounting Management Challenges** XYZ Corporation is a multinational company operating...

Accounting
Q

Consultex, Inc. was founded in 2012 as a small financial consulting business. The company had...

Accounting
Q

Use the following situation to calculate amounts to be withheld from the employee's earnings for...

Accounting
Q

Entries for stock dividends Madrid Corporation has 26,000 shares of $20 par common stock outstanding....

Accounting
Q

need help!! Home Ownership: Rent Versus Own Your...

Accounting
Q

NYSE: EPAM Write a thoughtful analysis of your stock and tell me if you would...

Finance
Q

Scenario: You are the financial consultant for a young couple who is in need of...

Finance